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Incorporation of statistical length scale into Weibull strength theory for composites

机译：将统计长度尺度纳入复合材料的威布尔强度理论

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In this paper an extension of Weibull theory by the introduction of a statistical length scale is presented. The classical Weibull strength theory is self-similar; a feature that can be illustrated by the fact that the strength dependence on structural size is a power law (a straight line on a double logarithmic graph). Therefore, the theory predicts unlimited strength for extremely small structures. In the paper, it is shown that such a behavior is a direct implication of the assumption that structural elements have independent random strengths. By the introduction of statistical dependence in the form of spatial autocorrelation, the size dependent strength becomes bounded at the small size extreme. The local random strength is phe-nomenologically modeled as a random field with a certain autocorrelation function. In such a model, the autocorrelation length plays the role of a statistical length scale. The focus is on small failure probabilities and the related probabilistic distributions of the strength of composites. The theoretical part is followed by applications in fiber bundle models, chains of fiber bundle models and the stochastic finite element method in the context of quasibrittle failure.
机译：本文介绍了威布尔理论的扩展，引入了统计长度量表。经典的威布尔强度理论是自相似的。强度对结构尺寸的依赖性是幂定律（双对数图上的直线）这一事实可以说明这一特征。因此，该理论预测极小的结构具有无限的强度。在本文中，表明这种行为是对结构元素具有独立随机强度的假设的直接暗示。通过以空间自相关的形式引入统计依存关系，与尺寸有关的强度在较小的尺寸极限处变得有限。局部随机强度在现象学上被建模为具有一定自相关函数的随机场。在这种模型中，自相关长度起着统计长度尺度的作用。重点是小的失效概率和复合材料强度的相关概率分布。理论部分之后是在纤维束模型，纤维束模型链和准有限元失效情况下的随机有限元方法中的应用。

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